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A certain musical scale has has 13 notes, each having a [#permalink]
01 Jan 2004, 22:34

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This post received KUDOS

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Difficulty:

95% (hard)

Question Stats:

48% (03:36) correct
52% (02:13) wrong based on 193 sessions

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

Re: OG PS #434-- musical scale [#permalink]
02 Jan 2004, 01:49

2

This post received KUDOS

stoolfi wrote:

On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

let the constant be k

F1 = 440

F2 = 440k

F3 = 440 k * k = 440 * k^2

F13= 440 * k^12

we know F13 = 2 *F1 = 2 * 440 = 880

880/440 = k^12

k = twelfth root of 2

for F7...

F7 = 440 * k^6 ( as we wrote for F2 and F3)
F7 = 440 * (twelfth root of 2) ^ 6

Re: OG PS #434-- musical scale [#permalink]
09 Nov 2011, 03:00

Praetorian wrote:

stoolfi wrote:

On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

let the constant be k

F1 = 440

F2 = 440k

F3 = 440 k * k = 440 * k^2

F13= 440 * k^12

we know F13 = 2 *F1 = 2 * 440 = 880

880/440 = k^12

k = twelfth root of 2

for F7...

F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6

F7 = 440 * sqrt (2)

Answer A

The question stem says that : the ratio of frequency to next higer frequency is fixed constant ...

Doesnt that mean F1/F2 = k

F2/F3 = k^2 and something like that .....???and not F2/F1 = k which is F2 = kF1???

Re: On another thread, someone with a very good GMAT score said [#permalink]
09 Nov 2011, 21:27

Siddhans,

It says the ratio of a frequency to the next higher frequency is a constant. f2/f1=f3/f2=f4/f3=.....=fixed number. This is an example of a geometric progression.

Re: OG PS #434-- musical scale [#permalink]
22 Feb 2013, 03:38

Praetorian wrote:

stoolfi wrote:

On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

let the constant be k

F1 = 440

F2 = 440k

F3 = 440 k * k = 440 * k^2

F13= 440 * k^12

we know F13 = 2 *F1 = 2 * 440 = 880

880/440 = k^12

k = twelfth root of 2

for F7...

F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6

Re: A certain musical scale has has 13 notes, each having a [#permalink]
22 Feb 2013, 04:48

Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2 ---------------- 1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A _________________

Re: OG PS #434-- musical scale [#permalink]
22 Feb 2013, 05:12

Expert's post

karmapatell wrote:

Praetorian wrote:

stoolfi wrote:

On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

let the constant be k

F1 = 440

F2 = 440k

F3 = 440 k * k = 440 * k^2

F13= 440 * k^12

we know F13 = 2 *F1 = 2 * 440 = 880

880/440 = k^12

k = twelfth root of 2

for F7...

F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6

F7 = 440 * sqrt (2)

Answer A

Why do you multiply and not add?

Like 1. 440 2. 440 + k and so on?

Because we are given that the ratio of a frequency to the next higher frequency is a fixed constant: F2/F1=k. _________________

Re: OG PS #434-- musical scale [#permalink]
22 Feb 2013, 09:29

karmapatell wrote:

Praetorian wrote:

stoolfi wrote:

On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

let the constant be k

F1 = 440

F2 = 440k

F3 = 440 k * k = 440 * k^2

F13= 440 * k^12

we know F13 = 2 *F1 = 2 * 440 = 880

880/440 = k^12

k = twelfth root of 2

for F7...

F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6

F7 = 440 * sqrt (2)

Answer A

Why do you multiply and not add?

Like 1. 440 2. 440 + k and so on?

"For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant"

The question says that the ratio of two consecutive frequencies is constant. Hence we multiply. _________________

Re: A certain musical scale has has 13 notes, each having a [#permalink]
22 Feb 2013, 12:59

Shoudln't "the ratio of a frequency to the next higher frequency is a fixed constant" be interpreted as f1/f2 = k instead of f2/f1=k? _________________

Alejandro LC MMT - EGADE Business School 2013 SM - HEC Paris 2014

Re: A certain musical scale has has 13 notes, each having a [#permalink]
12 Jul 2013, 21:40

Pushpinder wrote:

Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2 ---------------- 1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A

Pushpinder Ji I couldn't understand from here. Can u tell me please

Last edited by Bunuel on 12 Jul 2013, 23:28, edited 2 times in total.

Re: A certain musical scale has has 13 notes, each having a [#permalink]
12 Jul 2013, 23:38

1

This post received KUDOS

Expert's post

dasikasuneel wrote:

Pushpinder wrote:

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2 ---------------- 1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A

Pushpinder Ji I couldn't understand from here. Can u tell me please

Re: A certain musical scale has has 13 notes, each having a [#permalink]
26 Jul 2013, 04:50

Bunuel wrote:

dasikasuneel wrote:

Pushpinder wrote:

A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)

Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2 ---------------- 1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A

Pushpinder Ji I couldn't understand from here. Can u tell me please

Re: A certain musical scale has has 13 notes, each having a [#permalink]
24 Sep 2013, 19:12

In a geometric progression, the median is the geometric mean given by SQRT (First * Last). Here, First is 440, Last is 2*440 = 880 and 7th Note is the median, so it's value = SQRT (440*880) = SQRT (440*440*2) = 440*SQRT(2) A is correct.

gmatclubot

Re: A certain musical scale has has 13 notes, each having a
[#permalink]
24 Sep 2013, 19:12

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